# Question

The Human Resources Department at Gutierrez and Associates has developed an interviewing procedure for hiring new employees. Prior to the interview, the department head uses the candidate’s resume to assign a probability that the interview will show the candidate to be “excellent”, “good” or “fair.” Currently there are four applicants for an opening at the company. Probability assessments for the four are shown below:

The hire/no hire decision will be made as follows: If the first candidate interviewed is excellent, hire immediately; otherwise conduct the next interview. If the second candidate interviewed is excellent, hire that candidate immediately; otherwise conduct the next interview. If the next candidate is either excellent OR good, hire that candidate; otherwise conduct the final interview. Hire the final candidate unless that candidate is only fair. If it ends up that no one is hired in this first round of interviews, go back and give the job to the first person interviewed. It is decided that the interview order will be D, then B, then A, then C. Define the random variable here as “number of interviews conducted.” Let x represent the values of the random variable.

a. List the possible values for the random variable.

b. Show the full probability distribution for the random variable.

c. Compute the expected number of interviews.

d. Determine the expected number of interviews if the interview order is changed to A, D, C, B.

The hire/no hire decision will be made as follows: If the first candidate interviewed is excellent, hire immediately; otherwise conduct the next interview. If the second candidate interviewed is excellent, hire that candidate immediately; otherwise conduct the next interview. If the next candidate is either excellent OR good, hire that candidate; otherwise conduct the final interview. Hire the final candidate unless that candidate is only fair. If it ends up that no one is hired in this first round of interviews, go back and give the job to the first person interviewed. It is decided that the interview order will be D, then B, then A, then C. Define the random variable here as “number of interviews conducted.” Let x represent the values of the random variable.

a. List the possible values for the random variable.

b. Show the full probability distribution for the random variable.

c. Compute the expected number of interviews.

d. Determine the expected number of interviews if the interview order is changed to A, D, C, B.

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